We assess the performance of real-time time-dependent density functional theory (RT-TDDFT) for the calculation of absorption spectra of 12 organic dye molecules relevant to photovoltaics and dye-sensitized solar cells with 8 exchange-correlation functionals (3 traditional, 3 global hybrids, and 2 range-separated hybrids). We compare the calculations with traditional linear-response (LR) TDDFT and experimental spectra. In addition, we demonstrate the efficacy of the RT-TDDFT approach to calculate wide absorption spectra of two large chromophores relevant to photovoltaics and molecular switches. RT-TDDFT generally requires longer simulation times, compared to LR-TDDFT, for absorption spectra of small systems. However, it becomes more effective for the calculation of wide absorption spectra of large molecular complexes and systems with very high densities of states.